Use Newton's method to approximate the given number correct to eight decimal places. ^4 squareroot 78
Answers
After three iterations, we have obtained an approximation to ^4√78 with an error of less than 8 decimal places. The final answer is: ^4√78 ≈ 3.14960699
Newton's method to approximate a number with given steps is a process in which successive approximations are computed.
It is possible to use Newton's method to approximate the value of ^4 √78 to 8 decimal places.
So, let's begin.
Approximation of ^4√78
The Newton-Raphson method is a numerical method that can be used to find the roots of an equation. It is based on the assumption that a differentiable function f(x) can be approximated by a tangent line at a point c.
The Newton-Raphson formula is given by:
xn+1=xn-f(xn)f'(xn)
In the case of our problem, we have the equation:
y = f(x) = x^4 - 78
We want to find the root of this equation.
Starting from an initial guess x0, we use the Newton-Raphson formula to compute xn+1 until we reach a desired level of accuracy.
We can start with an initial guess x0 = 3, which is a number close to the actual value of the root. We can now apply the formula with x0 = 3, and iterate until we obtain the desired accuracy.
x1 = 3 - (3^4 - 78) / (4 * 3^3)
= 3.1496598639x2
= 3.1496598639 - (3.1496598639^4 - 78) / (4 * 3.1496598639^3)
= 3.1496069892x3
= 3.1496069892 - (3.1496069892^4 - 78) / (4 * 3.1496069892^3)
= 3.1496069892
We have used Newton's method to approximate ^4√78 to eight decimal places.
The final approximation is 3.14960699.
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Related Questions
Consider the spreadsheet below that lists the hours spent studying five subjects each week by five students. Each student studies for a total of 25 hours per week. Course Study Time Per Week total hours 25 studying Name Poly Sci Math Chemistry Comp Sci Psychology 6 Jonah 7 Barry 1 Samantha 9 Evan 10 Tricia 6.5 5.5 Suppose the above spreadsheet (A6:F10) is sorted according to this criteria: Poly Sci is the primary key sorted in descending order, and Psychology is the secondary key sorted in ascending order. What student name would be in cell A8?
-Evan
-Samantha
-Jonah
-Barry
-Tricia
Answers
Based on the given criteria for sorting the spreadsheet, the student name that would be in cell A8 is Jonah.
Based on the sorting criteria mentioned, the primary key for sorting is "Poly Sci" in descending order, and the secondary key is "Psychology" in ascending order.
Looking at the data in the "Poly Sci" column, we can see that the values are sorted in descending order as follows: 10, 9, 7, 6.5, 6.
Within the "Poly Sci" values of 6, the secondary key "Psychology" comes into play to determine the order. Among the students with a "Poly Sci" value of 6, we have Jonah and Tricia.
Comparing their "Psychology" values, we can see that Jonah has a "Psychology" value of 6, while Tricia has a "Psychology" value of 5.5.
Since the secondary key "Psychology" is sorted in ascending order, Jonah should appear before Tricia.
Therefore, the student name that would be in cell A8 is Jonah.
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67×73=1×3(mod 5)show works
Answers
Answer
Check Explanation
Explanation
a ≡ b (mod n)
This means a and b have the same remainder when they are divided by n
So, to check if this question works out, we divide what is on the left hand side and what is on the right hand side by what is after the mod.
1) 67 × 73 ≡ 1 × 3 (mod 5)
4891 ≡ 3 (mod 5)
So, to check,
(4891/5) = 978 remainder 1
(3/5) = 0 remainder 3
The remainders are different.
So, this equation is wrong and does not work.
This equation is false.
2) 83¹⁴⁴ ≡ 15¹⁴⁴ (mod 17)
Noting that it is the units digit that determines the remainder
3 raised to the power of a multiple of 4 gives 81 raised to the power of a positive integer
5 raised to power of a multiple of 4 gives 625 raised to the power of a positive integer
So, using these numbers,
83¹⁴⁴ ≡ 15¹⁴⁴ (mod 17)
81 ≡ 625 (mod 17)
(81/17) = 4 remainder 13
(625/17) = 36 remainder 13
The remainders are the same.
So, this equation is correct and it works.
This equation is true.
Hope this Helps!!!
A shoe store recorded the price (in dollars) of 175 pairs of women's shoes and 175 pairs of men's shoes. The data collected was used to create the following table.
Picture
Which statement accurately describes the difference in the price of men's and women's shoes at this store?
The price of women's shoes varies less than men's shoes.
Most of the men's shoes in the data set cost more than women's shoes.
Most of the women's shoes in the data set cost more than men's shoes.
The price of men's shoes has a higher interquartile range than that of women's shoes.
Answers
Answer:
Most of the men's shoes in the data set cost more than women's shoes.
Step-by-step explanation:
From what I could tell it can't be The price of men's shoes has a higher interquartile range than that of women's shoes. becuse that's false what looks to fit is Most of the men's shoes in the data set cost more than women's shoes. since on the graph more of the mens vaules are bigger
Plot a point on the coordinate plane to represent each of the ratio values in the table.
Time (s)Distance (m)
A table displaying Time in seconds in one column and Distance in meters in the other. The time column contains 1, 2, 4, and 6. The distance column contains 3, 6, 12, and 18.
Answers
Answer:
Refer the attached graph.
Step-by-step explanation:
Given : Time (h) Distance (km) able displaying Time in hours in one column and Distance in kilometers in the other. The time column contains 1, 3, 6, and 9. The distance column contains 2, 6, 12, and 18.
To plot : The points on the coordinate plane.
Solution :
Time is independent variable so it is taken on x-axis.
Distance is taken on y-axis.
x y
1 2
3 6
6 12
9 18
When we plot these points in the coordinate plane, we get a linear equation.
The linear equation form is
Refer the attached graph.
Step-by-step explanation:
Plot a point on the coordinate plane to represent each of the ratio values in the table shows me how to point the ratio values in the table
answer the question please i would appreciate it man
Answers
The scientific notation representation is 2.6 x \(10^{-2}\).
What is scientific Notation?Scientific notation is a way to present extremely large or extremely small numbers in a more understandable way. We are aware that full numbers can go on forever, but we are unable to write such enormous figures on paper. Additionally, a simpler method of representation was required for the numbers that appear at the millions place after the decimal. This makes it challenging to represent a small number of integers in their enlarged form. We therefore employ scientific notations.
Given:
(0. 00032) (5.2 x \(10^6\))/ 6.4 x \(10^5\)
Now, solving the above expression
= 0.001664 x 10² / 6.4
= 0.00026 x 10²
= 2.6 x \(10^{-2}\)
Hence, the scientific notation representation is 2.6 x \(10^{-2}\).
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Someone please help me with this question
Answers
Answer:
see below
Step-by-step explanation:
(w+14)/2 = 10
Multiply each side by 2
(w+14)/2 *2 = 10*2
w+14 = 20
Subtract 14 from each side
w+14-14 = 20-14
w = 6
Answer:
20
6
Step-by-step explanation:
(w + 14)/2 = 10
w + 14 = 2(10)
w + 14 = 20
w = 20 - 14
w = 6
Parallelogram OPQR is such that OP = (-7,24) and OR = (-8,-1). A. Determine the angle between the vectors OR and OP B. Determine the acute angle between the diagonals OQ and RP
Answers
A 2-column table with 6 rows. The first column is labeled x with entries negative 2, negative 1, 0, 1, 2, 3. The second column is labeled f of x with entries 20, 0, negative 6, negative 4, 0, 0.
Which is an x-intercept of the continuous function in the table?
(–1, 0)
(0, –6)
(–6, 0)
(0, –1)
Answers
An x-intercept is a point where the graph of a function crosses the x-axis, meaning the corresponding y-value is zero. To find the x-intercepts from the given table, we look for entries in the second column (f(x)) where the value is zero.
Looking at the second column, we can see that the function f(x) has an x-intercept at x = -1 since f(-1) = 0. Therefore, the correct x-intercept from the options provided is (-1, 0).
it costs $20 per day to board a dog and $16 per day to board a cat. The kennel needs to make at least $800 per day to cover expenses, but can hold no more than 80 total animals. Write a systems of inequalities, graph , and give two possible solutions to the number of dogs and cats they can board each day
Answers
Answer:
Step-by-step explanation:
the anwer is r=dog y=cat 20r+16y>800-->y>-5/4 r+50 20r-16y<r+80 40 dogs+20 cats 15+55 cats
Use computational and algebraic tools to quantify the total costs (gas, maintenance/repairs, purchase price) for each scenario over the three years.
Round your answers to the nearest dollar.
Scenario
Total Cost for Three Years
Keep the old car
$
Number
Buy the fuel-efficient used car
$
Number
Step 1: Understand the Problem
Keep the Old Car or Buy a Used Car
Manny is an online student who currently owns an older car that is fully paid for. He drives, on average, 170 miles per week to commute to work. With gas prices currently at $ 2. 22 per gallon, he is considering buying a more fuel-efficient car, and wants to know if it would be a good financial decision.
The old car Manny owns currently gets 20 miles per gallon for average fuel efficiency. It has been a great vehicle, but with its age, it needs repairs and maintenance that average $ 690 per year (as long as nothing serious goes wrong).
The newer, more fuel-efficient car that he is looking at to purchase will cost a total of $ 8,000 over a three-year loan process. This car gets 35 miles per gallon and would only require an average of $ 30 per month for general maintenance. To help make a decision, Manny wants to calculate the total cost for each scenario over three years. He decides to use the quantitative reasoning process to do this
Answers
Based on the total costs over three years, keeping the old car would be more financially favorable for Manny compared to buying the fuel-efficient used car.
Let's calculate the total costs for each scenario over three years:
Keep the old car:
Gas cost: Manny drives an average of 170 miles per week, which is approximately 8,840 miles per year (170 miles/week * 52 weeks/year). With an average fuel efficiency of 20 miles per gallon, he would need 442 gallons of gas per year (8,840 miles / 20 miles per gallon). At a gas price of $2.22 per gallon, the annual gas cost would be approximately $981 (442 gallons * $2.22/gallon). Over three years, the total gas cost would be $2,943 ($981 * 3).
Maintenance/repairs cost: The average annual maintenance/repairs cost is $690. Over three years, the total maintenance/repairs cost would be $2,070 ($690 * 3).
Total cost for keeping the old car over three years: Gas cost + Maintenance/repairs cost = $2,943 + $2,070 = $5,013.
Buy the fuel-efficient used car:
Gas cost: With a fuel efficiency of 35 miles per gallon, Manny would need approximately 252 gallons of gas per year (8,840 miles / 35 miles per gallon). The annual gas cost would be approximately $559 (252 gallons * $2.22/gallon). Over three years, the total gas cost would be $1,677 ($559 * 3).
Maintenance/repairs cost: The monthly maintenance cost is $30, which translates to an annual cost of $360 ($30 * 12 months). Over three years, the total maintenance/repairs cost would be $1,080 ($360 * 3).
Purchase price: The purchase price of the used car is $8,000.
Total cost for buying the used car over three years: Gas cost + Maintenance/repairs cost + Purchase price = $1,677 + $1,080 + $8,000 = $10,757.
Comparing the total costs:
Keep the old car: $5,013
Buy the used car: $10,757
Based on the total costs over three years, keeping the old car would be more financially favorable for Manny compared to buying the fuel-efficient used car.
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write a formula for a linear function f(x) that models the situation, where x is the number of years after 2007. in 2007 the average adult ate 52 pounds of chicken. this amount will increase by 0.8 pounds per year until 2012.
Answers
Step-by-step explanation:
x = number of years after 2007.
x = 0 for 2007.
PC(x) is a function that calculates how many pounds of chicken the average adult will eat every year (x) after 2007 (up to 2012).
PC(x) = 0.8x + 52
0 <= x <= 5
in 2007 (x = 0) the average adult ate 52 pounds.
in every year after 2007 until 2012 0.8 pounds get added to the amount of the previous year.
so, in 2012 (x = 5) the average adult will eat
PC(5) = 0.8×5 + 52 = 4 + 52 = 56 pounds of chicken.
while shopping kyla found a dress that she would like to purchase but it costs more than she has kyla charges $5.50 aam hour for babysitting she wants to figure out how many hours she must babysit to earn $52.25 to buy the dress
Answers
Complete the steps in solving the quadratic function 7x – 9 = 7x2 – 49x by completing the square.
–9 = 7x2 –
x
–9 +
= 7(x2 – 8x +
)
Answers
Answer:The steps in solving the quadratic function 7x – 9 = 7x^2 – 49x by completing the square are as follows:
Add and subtract (49/2)^2 = (36) to the right-hand side of the equation to complete the square. This gives us:
7x - 9 = 7x^2 - 49x + 36
Factor out the coefficient of the x^2 term, which is 7, on the right-hand side of the equation. This gives us:
7x - 9 = 7(x^2 - 7x + 6)
Take the square root of the number inside the parenthesis and add and subtract it, to get:
7x - 9 = 7(x - 3.5)^2 - 2.25
Now we can add 9 to both sides of the equation to get:
7x = 7(x - 3.5)^2 + 0.75
Now we can divide both sides by 7 to get:
x = (x - 3.5)^2 + 0.75/7
Now we can solve the equation by taking the square root of both sides and adding and subtracting 3.5 to get:
x = 3.5 ± √(x^2 - 7x + 6)
Now we have our solutions, x = 3.5 + √(x^2 - 7x + 6) and x = 3.5 - √(x^2 - 7x + 6) which are the solutions of the quadratic equation.
Step-by-step explanation:
Answer:
56, 112, 16
Step-by-step explanation:
I just know
2 a. How many hypotheses are used for each experiment? b. What name do they go by? c. Which one are we actually testing?
Answers
(a) Two-hypothesis are used for each experiment,
(b) They go by the names of Null and Alternate Hypothesis.
(c) We actually test the Alternate hypothesis.
Part(a) : In most experimental designs, there are two hypotheses: the null hypothesis (H₀) and the alternative hypothesis (Hₐ).
Part(b) : The Hypotheses are generally classified as "Null-Hypotheses" or "Alternative-Hypotheses".
The "Null-Hypothesis" (H₀) is defined as a statement that assumes there is no significant difference or relationship between variables or that an intervention has no effect.
The "Alternative-Hypothesis" (Hₐ) is defined as a statement that assumes there is a significant difference or relationship between variables or that an intervention has an effect.
Part (c) : The hypothesis being-tested in an experiment is generally the "Alternative-Hypothesis" (Hₐ) because the "Null-Hypothesis" (H₀) is assumed to be true until evidence is found to reject it.
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The given question is incomplete, the complete question is
(a) How many hypothesis are used for each experiment?
(b) What name do they go by?
(c) Which one we actually test?
what is 7/9 divided by 6/8
Answers
Answer: \(\frac{28}{27}\) or \(1\frac{1}{27}\)
Step-by-step explanation:
\(\frac{7}{9} /\frac{6}{8} = \frac{7}{9}(\frac{8}{6})\)
\(\frac{7}{9} (\frac{8}{6} ) = \frac{28}{27}\)
\(\frac{28}{27} = 1 \frac{1}{27}\)
The equation x2 - 7x=0 when solved is:
Answers
Answer:
x =0 x=7
Step-by-step explanation:
x^2 - 7x=0
Factor out an x
x(x-7) =0
Using the zero product property
x =0 x-7 =0
x =0 x=7
Describe two similar polygons in your home. How do you know they
are similar?
Answers
By comparing the corresponding angles and side lengths, we can conclude that the square and rectangle in my home are similar polygons. The similarity is based on their shared shape and the proportional relationship between their corresponding side lengths.
In my home, I have two similar polygons: a square and a rectangle. These polygons can be considered similar because they have the same shape, but their sizes may be different.
To determine if two polygons are similar, we need to compare their corresponding angles and corresponding side lengths. In the case of the square and rectangle in my home:
Corresponding angles: Both the square and rectangle have right angles at each corner, which means their corresponding angles are equal.
Corresponding side lengths: While the square has all four sides of equal length, the rectangle has two pairs of opposite sides of equal length. However, even though their side lengths are not identical, the ratios between the side lengths are the same. For example, in a square, all sides are equal, let's say length "a". In a rectangle, two opposite sides are equal, let's say length "a", and the other two sides are equal, let's say length "b". The ratio of the side lengths in both polygons is a:b, which remains constant.
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Please help I am confued
Answers
Answer:
50
40
You have them right
Step-by-step explanation:
If he is charging 40 per hour, take away 40 from 90 because this is the first hour. Meaning at hour 0, there are 50 dollars.
there are only blue, yellow and green cubes in a bag. there are three times as many blue cubes than yellow cubes and five times as many green cubes then blue cubes. what is the chance that Sarah will get the yellow cube in its simplest form.
Answers
Answer: 1/11
Step-by-step explanation:
Let x be no. of yellow cubes.
Blue = 2x
Green = 4 x 2x = 8x
Total cubes = x + 2x + 8x = 11x
P(yellow) = x / 11x = 1/11
In a city of 26000 populations, 5000 read English newspaper, 12000 read Nepali newspaper and 1000 read both. What percentage read neither English and Nepali newspaper? ( from set theory )
Answers
Answer:
38.46%
Step-by-step explanation:
total readers=16000
population=26000
no of non-readers=total population-total readers
=26000-16000
=10000
percentage of non-readers=non-readers×100%
population
=10000×100%
26000
percentage of non-readers is 38.46%
each character in a password is either a digit [0-9] or lowercase letter [a-z]. how many valid passwords are there with the given restriction(s)? length is 19.
Answers
There are C( 32,15) * P( 19,19) valid passwords.
Given digit = 0,1,2,3,4,5,6,7,8,9
Letter from a to z = a,b,c,d,......, x,y,z
Total of both digits and letters = 10+26
= 36
In this question it started that,
length is 19, and No characters repeated.
Must contain: z, 1, 0 and 9.
Therefore, since all password must include z,1,0,9.
Lets denote the four of them as Ф.
These four notations must be included and the remaining 15
[ i.e., (19 -Ф)] is selected from the whole 32 characters as C( 32,15).
Also, 15 and Ф can be arranged as ¹⁹P₁₉ = 191 ways.
Therefore, the total permutation are:
C( 32,15) * P( 19,19)
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Complete the patterns of the equivalent ratios by filling in the gaps.
27:9
_ : 7
15:5
9 : _
3 : _
Answers
9:3
3:1
there all a 3:1 ratio
a gym class has $12$ students, $6$ girls and $6$ boys. the teacher has $4$ jerseys in each of $3$ colors to mark $3$ teams for a soccer tournament. if the teacher wants at least one girl and at least one boy on each team, how many ways can he give out the jerseys? (jerseys of the same color are indistinguishable.)
Answers
So, the teacher can give out the jerseys in 840 ways.
The teacher wants to divide the 12 students into 3 teams, each with at least one girl and one boy.
One possible way to count the number of ways to divide the students is to use the stars and bars method.
For the first team, we have 5 stars and 2 bars, so the number of ways to pick 6 students is:
(5+2)!/(5!2!) = 7
For the second team, we have 4 stars and 1 bar, so the number of ways to pick 6 students is:
(4+1)!/(4!1!) = 5
For the third team, we have 3 stars, so the number of ways to pick 6 students is:
(3+0)!/(3!0!) = 4
Then we can multiply the number of ways to pick students for each team together to find the total number of ways to divide the students:
7 * 5 * 4 = 140
Then, as the jerseys are indistinguishable, we just have to multiply the number of ways to divide the students by the number of ways to distribute jerseys:
140 * 3! = 840
Therefore, the teacher can give out the jerseys in 840 ways.
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What is the solution to the equation? −6 = x/8 Enter your answer in the box. x = ?
Answers
Answer:
-48
Step-by-step explanation:
-6=x/8
-6×8=x
x=-48
What is the solution to the equation? −6 = x/8 Enter your answer in the box. x = ?
The solution to the equation is: -48
------------Verified Commentry from a K12 Representitive------------
If tan(t)=4/9 what is tan(t−π)
Answers
The value of tan(t−π) is 4/9.
According to the statement
we have given that tan(t)=4/9 and we have to find the value of tan(t−π).
So,
tan(t−π) -(1)
take negative sign common from equation (1) it then
tan(t−π) = -tan(-t+π)
and we know that the according to the mathematics formula it become
tan(-t+π) is -tan t
then
tan(t−π) = -(-tan t)
it becomes
tan(t−π) = tan t
then its value becomes
tan(t−π) = tan(t)=4/9.
because we have given that the value of tan t is tan(t)=4/9.
So, The value of tan(t−π) is 4/9.
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An ordered pair is a(n) ________ of an equation in two variables if replacing the variables by the coordinates of the ordered pair results in a true statement.
Answers
An ordered pair is a solution of an equation in two variables if replacing the variables by the coordinates of the ordered pair results in a true statement.
In mathematics, an equation in two variables represents a relationship between two quantities. An ordered pair consists of two values, typically denoted as (x, y), that represent the coordinates of a point in a two-dimensional plane.
When these values are substituted into the equation, if the equation holds true, then the ordered pair is considered a solution or a solution set to the equation. This means that the relationship described by the equation is satisfied by the values of the ordered pair. In other words, the equation is true when evaluated with the values of the ordered pair.
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Ethan is 1.85 meters tall. At 10 a.m., he measures the length of a tree's shadow to be 28.45 meters. He stands 24.3 meters away from the tree, so that the tip of his shadow meets the tip of the tree's shadow. Find the height of the tree to the nearest hundredth of a meter.
Answers
The height of the tree that casts a shadow is 28.45 meters will be 12.68 meters.
What is the triangle?The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.
The ratio of the matching sides will remain constant if two triangles are comparable to one another.
Ethan is 1.85 meters tall. At 10 a.m., he measures the length of a tree's shadow to be 28.45 meters. He stands 24.3 meters away from the tree.
Then the height of the tree is given as,
h / 1.85 = 28.45 / (28.45 - 24.3)
h / 1.85 = 28.45 / 4.15
h = 1.85 x 28.45 / 4.15
h = 12.68 meters
The height of the tree that casts a shadow is 28.45 meters will be 12.68 meters.
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PLS HELP ME This IS HARD
Find the value of cos
�
H rounded to the nearest hundredth, if necessary.
Answers
Answer:
Step-by-step explanation:
Cos0 = adj/hyp
cos0 = 40/41
find the inverse cos of that.
0 = cos^-1(40/41)
0 = 12.68
Find the inverse function in slope-intercept form (mx+b):
f(x) = -x + 6
Answers
switch the variables
x = -y + 6
x - 6 = -y
-x + 6 = y
a couple plans to have three children. find the probability of having all boys. find the probability of having two boys or two girls.
Answers
the find the probability of having two boys or two girls will be 50%
What is probability ?
The probability formula can be used to calculate the likelihood of an event by simply dividing the favorable number of possibilities by the total number of options. The likelihood of an occurrence might vary from 0 to 1 because the favourable number of outcomes can never be greater than all possible outcomes.
For two genders and three children, there are a total of 2³=8 potential combinations.
There are (GGG, GGB, BGG, GBG) = 4 pairs where at least two of the children are female.
As a result, there is a 4/8 = 1/2 chance that the family of three children will include at least two girls.
Hence the find the probability of having two boys or two girls will be 50%.
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